This report covers the research conducted from September 1996 to August 1997 (eighteen months into the three year grant). We have obtained a number of significant findings based on the on the work that we have conducted under this grant during the past year. As we stated in our original proposal the work has focused on multi-dimensional models of the convective epoch in core collapse supernovae. During the past year we have developed a large number of models of the convective epoch in 2-D under two levels of neutrino transport approximation and we are currently working on 3-D models. In the following pages will endeavor to give brief descriptions of our results.